A P E D

ACCURACY OF PREDICTION EQUATIONS FOR
DETERMINING ONE REPETITION MAXIMUM BENCH
PRESS IN WOMEN BEFORE AND AFTER RESISTANCE
TRAINING
JERRY L. MAYHEW,1,2 BLAIR D. JOHNSON,3 MICHAEL J. LAMONTE,4 DIRK LAUBER,5
6
AND WOLFGANG KEMMLER
1
Human Performance Laboratory, Truman State University, Kirksville, Missouri; 2Department of Physiology, A.T. Still
University of Health Sciences, Kirksville, Missouri; 3Exercise Science Department, University of Wisconsin–LaCrosse, LaCrosse,
Wisconsin; 4Department of Social and Preventive Medicine, University of Buffalo, Buffalo, New York; 5Institute of Sport Sciences
and 6Institute of Medical Physics, University of Erlangen, Erlangen, Germany
ABSTRACT
Mayhew, JL, Johnson, BD, LaMonte, MJ, Lauber, D, and
Kemmler, W. Accuracy of prediction equations for determining
one repetition maximum bench press in women before and after
resistance training. J Strength Cond Res 22(5): 1570–1577,
2008—Repetitions to fatigue (RTF) using less than a 1 repetition maximum (1RM) load (RepWt) have been shown to be
a good predictor of 1RM strength in men, but such information
is scarce in women. The purpose of this study was to evaluate
the accuracy of current prediction equations to estimate 1RM
bench press performance and to determine whether resistance
training changes the capability to predict 1RM from muscular
endurance repetitions in young women. Members (n = 103) of
a required wellness course were measured for 1RM bench
press and RTF using randomly assigned percentages between
60% and 90% of the 1RM (RepWt) before and after 12 weeks
of progressive resistance training. The %1RM used to perform
RTF remained the same for each individual after training
(75.6% 6 10.3%) as before. One repetition maximum bench
press increased significantly after training (28% 6 21%).
Although the change in the group average for RTF (0.6 6 6.1)
was not significant, the correlation between pretraining and
posttraining RTF was moderate (r = 0.66; p , 0.01), and
individual differences in percentage change in RTF were
substantial (27% 6 99%). The percentage change in 1RM was
not significantly related to initial 1RM (r = 20.05), but it was
negatively related to the change in RTF (r = 20.40; p , 0.01).
Prediction equations were more accurate in the pretraining and
Address correspondence to Jerry L. Mayhew, e-mail: [email protected]
truman.edu.
22(5)/1570–1577
Journal of Strength and Conditioning Research
Ó 2008 National Strength and Conditioning Association
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posttraining conditions, in which fewer than 10 RTF were used.
Resistance training may alter the relationship between strength
and muscle endurance across a wide range of RTF in young
women without compromising the accuracy of predicting
maximal strength.
KEY WORDS muscle strength, muscle endurance, training
effect, performance prediction
INTRODUCTION
T
he most commonly used method for assessing
muscular strength is the 1 repetition maximum
(1RM), which is typically performed with free
weights. This approach requires an individual to lift
as much as possible once, through a full range of motion.
Although this type of assessment is considered the most
accurate way to determine maximal dynamic strength, there
are some inherent complications associated with it. Although
the 1RM approach is considered safe when performed
correctly (15,29), many novice individuals, especially women,
may be reluctant to continue adding weight to reach
a maximal value. The increase in load may produce a greater
risk for injury during free weight exercises, especially if
a participant is unaccustomed to moving heavy loads (29).
An untrained individual may also be intimidated by trying to
lift heavy loads due to the fear of failure. In addition, the
proper 1RM assessment may be very time-consuming
because adequate rest between attempts is required (40).
Another approach to determining maximal strength is to
estimate the 1RM by using repetitions performed to the point
of temporary muscle failure, which is termed repetitions to
fatigue (RTF). Using this method, a participant selects a load
that is believed to be less than his or her 1RM and performs as
many consecutive repetitions as possible. The load or RTF are
then applied to any of a number of available prediction
equations to estimate a 1RM value. Most of the current
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equations function best when using a load that will produce
a range of 2 to 10 repetitions, whereas other equations may be
applied by using up to 20 RTF (28). Although many of these
equations are reasonably accurate and precise, most of them
do not provide information on the population from which
they were developed. This is a concern for the use of these
prediction equations because the age, gender, and training
status of the individuals may affect the accuracy and precision
of the 1RM estimation (28).
Although there are some inherent problems with using
RTF and their subsequent prediction equations for the
determination of a participant’s 1RM, this approach may
also be very beneficial. For individuals who are unfamiliar
with strength training or testing, attempting a 1RM with
heavy loads may be a very intimidating task, whereas using
a lighter load and performing RTF may be a more welcoming
experience. An RTF technique can also be very efficient in
that it reduces the time spent testing and allows more time for
training (12). After a proper warm-up, only 1 set is needed to
predict a hypothetical 1RM (12), which can give an
approximation of maximal strength at any point along the
training continuum.
Another concern with currently available equations is
their application to women. Recent research has suggested
that women may not produce muscle fatigue at the same rate
that men do (16,17,35). If this is the case, women may be
able to produce more repetitions at a given %1RM or
produce an equivalent number of repetitions at a higher
%1RM. Because few of the currently available prediction
equations mention including women in their sample
(10,21,26,31,37), it raises the question of the applicability of
these equations to women. With the growing involvement
of women in resistance training, it would be advantageous
to strength and conditioning specialists to determine the
accuracy of RTF prediction equations for assessing the
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strength of women. Furthermore, limited information is
available on the effect of training on the relationship
between RTF and maximal strength. In men, several studies
have found that training does not alter the relationship
between muscle strength and endurance, and predictive
accuracy is not compromised (27,36). However, such
information is scarce in women. Therefore, the purpose
of this study was to evaluate the accuracy of current
prediction equations to estimate 1RM bench press performance and to determine whether resistance training
changes the capability to predict 1RM from muscular
endurance repetitions in young women.
METHODS
Experimental Approach to the Problem
This study explored the accuracy of using repetitions to
prediction 1RM bench press performance in young women
and the effect of moderate resistance training on that relationship. The subjects were typical of young women with limited
resistance training experience who underwent an introductory
level course of resistance training. The objective was to
determine whether any currently available prediction equations
were accurate for assessing maximal bench press strength both
before and after several weeks of resistance training.
Subjects
College women (n = 103) enrolled in university wellness
classes volunteered to participate after signing an Institutional
Review Board–approved informed consent document. Resistance training background of the participants ranged from
never having used weights to infrequent training over the
previous 2 years. Previous sports and work participation that
might have had a psychosocial bearing on the participation
of the subjects were not considered. The physical and performance characteristics of the participants are shown in Table 1.
TABLE 1. Physical and performance characteristics of the participants before and after resistance training (n = 103).
Before training
After training
Variable
Mean 6 SD
Range
Mean 6 SD
Range
t ratio
% change
Age (y)
Height (cm)
Weight (kg)
BMI (weight/height2)
1RM bench press (kg)
Bench presskg–1
Repetition weight (kg)
%1RM bench press
Bench press repetitions
19.1 6 1.2
166.0 6 6.1
61.6 6 8.8
22.3 6 3.4
28.7 6 6.7
0.48 6 0.10
21.5 6 4.6
75.6 6 10.3
12.5 6 6.9
18.0–25.3
152.0–185.0
45.1–92.5
16.8–31.5
18.2–61.4
0.27–0.79
13.6–36.4
56.3–92.9
2–20
19.3 6 1.2
166.3 6 6.2
62.7 6 8.7
22.6 6 3.4
36.4 6 8.4
0.59 6 0.12
27.3 6 6.1
75.6 6 10.3
13.1 6 7.8
18.2–25.5
152.2–185.4
46.5–91.0
17.3–31.1
22.7–63.6
0.36–0.92
13.6–43.2
60.0–94.1
1–30
10.88*
3.64*
3.66*
2.69*
14.55*
13.79*
14.35*
0.13
0.97
1.2
0.2
2.3
1.8
25.5
22.9
25.5
–0.4
9.7
% Change = posttraining value – pretraining value.
*p , 0.01.
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Procedures
Training Program. Each participant underwent a progressive
resistance training program 3 days per week for 12 weeks. The
resistance exercises performed were the supine bench press,
biceps curls, latissimus dorsi pull-downs, upright rows,
half-squats, and calf raises. Three sets of each resistance
exercise were performed in a modified linear periodization
format. During weeks 1 through 4, loads that produced
a range of 10 to 12 repetitions were used. During weeks 5
through 9, loads were increased to obtain a range of 8 to 10
repetitions for each exercise. During weeks 10 through 12,
participants were encouraged to increase the load for each
exercise to elicit a range of 5 to 7 repetitions. If a participant
was able to perform repetitions beyond the desired ranges for
each set of any given exercise, she was encouraged to increase
the load to re-establish the desired repetition range. In
addition, 2 sets of 20 to 25 repetitions of unweighted
abdominal curl-ups were performed at each session throughout the training program.
One Repetition Maximum Testing. A 1RM using the free weight
supine bench press exercise was used to assess upper-body
strength in each participant. Before the 1RM assessment, the
participants were given instructions on proper lifting techniques and assessment procedures. The participants were
instructed to lower the weight slowly, under control, until it
touched the chest but not to bounce the weight off their chest.
The participants’ shoulders, back, and buttocks were required
to remain in contact with the bench, and their feet were
required to remain on the floor throughout the exercise.
After a warm-up consisting of several sets of 6 to 10
repetitions using a light load, each participant attempted
a single repetition with a load she believed to be
approximately 90% of her maximum. If the attempt was
successful, weight was added depending on the ease with
which the single repetition was completed. If the attempt was
not successful, weight was removed from the bar. A minimum
of 5 minutes of rest was given between maximal attempts (40).
This procedure continued until the participant was not able
to complete a single repetition through the full range of
motion. The heaviest load completed using proper form was
determined to be the participant’s 1RM and was usually
achieved in 3 to 5 attempts. The reliability of this procedure
has previously been established at more than 0.98 (17,32).
Repetition Testing. The week after the 1RM assessments, each
participant was randomly assigned to lift a weight ranging
between approximately 60% and 90% of her 1RM. After an
adequate warm-up using a light load, the participants
performed repetitions to momentary muscular failure (i.e.,
RTF) with their assigned %1RM. After 12 weeks of training,
each participant performed RTF using the identical %1RM
that was used before training. The same lifting techniques
used during the 1RM testing were used for the RTF
assessments. The reliability of this procedure has previously
been established at 0.97 (32).
Prediction Equations. Fourteen 1RM prediction equations
using RTF identified from the literature were selected (Table
2). Most of the prediction equations gave no evidence of the
population used to develop the equations or how they were
derived statistically. Eight of the equations were linear
(3,4,6,7,10,23,24,41), and 4 were exponential (24,26,27,37). Of
these equations, only 5 (10,21,26,27,37) indicated that
women were included in their sample.
TABLE 2. Prediction equations to estimate 1 repetition maximum from repetitions to fatigue.
Source
Adams (3)
Berger (4)
Brown (6)
Brzycki (7)
Cummings and Finn (10)
Kemmler et al. (17)
Lander (19)
Lombardi (20)
Mayhew et al. (21)
O’Connor et al. (25)
Reynolds et al. (26)
Tucker et al. (31)
Wathen (33)*
Welday (35)
Equation
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
1RM
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
= RepWt/(1 –0.02 RTF)
= RepWt/(1.0261 –0.00262 RTF)
= (Reps 3 0.0338 + 0.9849) 3 RepWt
= RepWt/(1.0278 –0.0278 RTF)
= 1.175 RepWt + 0.839 Reps –4.29787
= RepWt (0.988 + 0.0104 RTF + 0.0019 RTF2–0.0000584 RTF3)
= RepWt/(1.013 –0.0267123 RTF)
= RTF0.13 RepWt
= RepWt/(0.522 + 0.419 e–0.055 RTF)
= 0.025 (RepWt 3 RTF) + RepWt
= RepWt/(0.5551 e–0.0723 RTF + 0.4847)
= 1.139 RepWt + 0.352 Reps + 0.243
= RepWt/(0.488 + 0.538 e–0.075 RTF)
= (RTF 3 0.0333) RepWt + RepWt
* Equation calculated from chart provided.
1 RM = 1 repetition maximum; RepWt = repetition weight, a load less than 1RM used to perform repetitions; RTF = repetitions to
fatigue.
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values. Pearson correlations were used to assess the degree
of relationship between selected variables. The 0.05 level was
accepted for statistical significance. Statistical power was
greater than 0.90, and the effect size was 0.95 for all analyses.
RESULTS
FIGURE 1. Comparison of muscular endurance repetitions before and
after training in women (n = 103).
Statistical Analyses
Paired t-tests were used to determine differences between
selected variables before and after training. A repeatedmeasures analysis of variance (ANOVA) was used to
determine the difference between predicted and actual
1RM performances. A repeated-measures ANOVA was also
used to assess the difference between actual strength
improvement and predicted strength improvement. Interclass
correlation coefficients (ICC) were used to evaluate the
degree of agreement between predicted and actual 1RM
The resistance training program increased the 1RM bench by
7.7 6 5.4 kg, or 28.2% 6 20.9%. Although the average change
in RTF after training was only 0.6, the range of change was
substantial (–15 to 17 repetitions) and caused the correlation
between pretraining and posttraining RTF to be only
moderate (r = 0.66; p , 0.001) and indicated considerable
variability in the response to training (Figure 1). The
pretraining 1RM bench press was not significantly related
to the change in 1RM (r = –0.05) or the change in RTF
(r = 0.13) but was significantly related to the percentage
change in 1RM (r = –0.30, p , 0.01).
Only 3 of the 14 equations produced predicted 1RM values
that were significantly different from the actual 1RM at the
pretraining and posttraining, when the full range of
repetitions was used. All of the predicted values were highly
correlated (p , 0.001) with the actual 1RM values, save for
the linear equations by Brzycki (7) and Lander (23) (Table 3).
At the pretraining, the equation by O’Conner et al. (30)
produced 67% of the predicted values within 62.3 kg of their
actual 1RM values and had a 95% confidence interval (CI) on
the difference between the predicted and actual 1RM of –5.9
TABLE 3. Accuracy of predicting 1 repetition maximum bench press in college women (n = 103) by using equations from
the literature.
Before training
Equation
Adams (3)
Berger (4)
Brown (6)
Brzycki (7)
Cummings and
Finn (10)
Kemmler et al. (17)
Lander (19)
Lombardi (20)
Mayhew et al. (21)
O’Connor et al. (25)
Reynolds et al. (26)
Tucker et al. (31)
Wathen (33)
Welday (35)
Actual 1RM (kg)
Predicted
Mean 6 SD
Constant error*
Mean 6 SD
% Error†
Mean 6 SD
After training
ICC
Predicted
Mean 6 SD
Constant error
Mean 6 SD
29.4
21.6
29.7
35.9
6 7.5
6 4.6§
6 6.9
6 24.6§
0.7
–7.1
0.9
7.2
6 4.2
6 3.9
6 2.9
6 23.7
2.9 6 16.1
–24.0 6 9.4
3.7 6 10.8
26.7 6 101.7
0.90‡
0.87‡
0.95‡
0.24§
38.2
27.5
37.9
46.9
6 10.2
6 6.0§
6 8.6
6 23.9§
1.7
–8.9
1.5
10.5
6 6.7
6 4.6
6 4.6
6 21.9
31.4
27.3
35.0
27.1
28.9
28.0
29.6
29.1
30.0
30.1
28.7
6 6.7
6 6.2
6 18.2§
6 5.7
6 6.2
6 6.2
6 6.8
6 5.1
6 6.9
6 7.0
6 6.7
2.7
–1.5
6.3
–1.6
0.2
–0.8
0.8
0.4
1.3
1.4
6 4.2
6 2.6
6 16.8
6 3.1
6 2.6
6 2.6
6 2.8
6 3.0
6 2.9
6 4.2
10.8 6 16.9
–4.7 6 9.1
22.9 6 70.7
–4.9 6 9.7
1.2 6 9.0
–2.1 6 9.0
3.4 6 10.4
2.8 6 10.1
4.9 6 10.5
5.3 6 11.0
0.89‡
0.96‡
0.40‡
0.93‡
0.96‡
0.96‡
0.96‡
0.93‡
0.96‡
0.95‡
38.7
34.6
46.1
34.2
36.8
35.7
37.7
35.9
38.2
38.5
36.4
6 7.6
6 7.5
6 21.4§
6 6.9
6 7.6
6 7.7
6 8.4
6 6.4
6 8.5
6 8.8
6 8.4
2.3
–1.8
9.7
–2.2
0.7
–0.7
1.3
–0.5
1.8
2.1
6 4.8
6 3.8
6 19.1
6 3.8
6 3.4
6 3.7
6 4.3
6 3.7
6 4.3
6 4.6
% Error
Mean 6 SD
5.4 6
–23.9 6
4.9 6
29.3 6
ICC
18.2
9.3
13.4
60.0
0.85‡
0.89‡
0.92‡
0.41‡
7.9 6 14.4
–4.2 610.0
27.1 6 52.2
–5.1 6 9.6
1.8 6 9.4
–1.2 6 9.8
4.2 6 11.7
0.0 6 9.5
5.7 6 11.8
6.5 6 12.5
0.90‡
0.94‡
0.47‡
0.93‡
0.95‡
0.94‡
0.93‡
0.93‡
0.93‡
0.92‡
ICC = interclass correlation coefficient; 1RM = 1 repetition maximum.
*Predicted 1RM –Actual 1RM.
†(Predicted – Actual)/Actual 3 100.
‡p ,0.01.
§p ,0.05.
VOLUME 22 | NUMBER 5 | SEPTEMBER 2008 |
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to 4.3 kg. At the posttraining, the equation by O’Connor et al.
(30) produced 57% of the predicted values within 62.3 kg of
their actual 1RM values and had a 95% CI on the difference
between the predicted and actual 1RM of –4.9 to 5.3 kg.
Because many of the existing prediction equations were
designed to be used when the repetition range was between
2 and 10, participants at both the pretraining and the
posttraining measurements who performed repetitions in that
range were evaluated (Table 4). At the pretraining, 9
equations produced predicted 1RM values that were not
significantly different from and significantly correlated with
the actual 1RM. The equation by Lombardi (24) produced
61% of the predicted values within 62.3 kg of their actual
1RM values and had a 95% CI on the difference between the
predicted and actual 1RM of –5.4 to 4.8 kg. At the
posttraining, 5 equations produced predicted 1RM values
that were not significantly different from and significantly
correlated with the actual 1RM. The equations by Adams (3),
Brzycki (7), Cummings and Finn (10), Lombardi (24), and
O’Conner et al. (30) produced the highest number of
participants with predicted values within 62.3 kg of their
actual 1RM values (i.e., 58% each). Four of the equations
(10,21,33,35) produced predicted 1RM values that were not
significantly different from actual 1RM values at either the
pretraining or the posttraining (Table 4).
A major concern when using a predicted 1RM to determine
the improvement from a resistance training program is the
degree of agreement between the changes in predicted values
(DP) versus the changes in actual values (DA). Although none
of the DP were significantly different from the DA, the ICCs
between the 2 values ranged from –0.09 to 0.95. Further
scrutiny of the plots between DP and DA revealed that the
equation by Tucker et al. (37) produced a high correlation
between the two (ICC = 0.87; p , 0.001) and had 65% of the
participants with DP values within 62.3 kg of their DA
(Figure 2).
A significant negative correlation between DA and DRTF
(r = –0.55; p , 0.001) indicated that greater increases in
strength were associated with greater decreases in the
number of RTF the women were able to perform with the
same %1RM after training (Figure 3). There was a moderate
tendency for those women who performed more RTF at the
pretraining to decrease more in RTF after training (r = –0.29;
p , 0.01). The change in RTF after training was not significantly correlated with body mass (r = 0.00) or pretraining
strength (r = 0.13).
DISCUSSION
A limited number of strength prediction studies have
acknowledged including women as participants. Several
TABLE 4. Accuracy of predicting 1RM bench press in college women using no more than 10 RTF and equations from the
literature.
Before training (n = 46)
After training (n = 45)
Equation
Predicted
bench press
Mean 6 SD
Constant
error*
Mean 6 SD
% Error†
Mean 6 SD
ICC
Adams (3)
Berger (4)
Brown (6)
Brzycki (7)
Cumming and Finn (10)
Kemmler et al. (17)
Lander (19)
Lombardi (20)
Mayhew et al. (21)
O’Connor et al. (25)
Reynolds et al. (26)
Tucker et al. (31)
Wathen (33)
Welday (35)
Actual 1RM (kg)
26.5 6 4.9‡
22.9 6 4.0‡
27.5 6 5.2
27.2 6 5.3
28.1 6 5.3
25.8 6 4.9‡
27.5 6 5.3
27.5 6 5.0
28.2 6 5.2
26.7 6 4.9‡
27.5 6 5.3
28.8 6 5.1‡
28.0 6 5.4
27.9 6 5.3
27.8 6 4.8
–1.3
–4.9
–0.3
–0.6
0.3
–1.9
–0.3
–0.3
0.4
–1.1
–0.2
1.0
0.2
0.1
–4.5 6 9.1
–17.4 6 7.2
–1.0 6 10.0
–2.0 6 10.5
1.1 6 10.6
–6.9 6 8.9
–1.1 6 10.5
–0.9 6 9.2
1.6 6 9.4
–3.7 6 9.1
–0.9 6 10.4
3.9 6 8.6
0.7 6 10.6
0.5 6 10.2
0.92§
0.92§
0.92§
0.91§
0.91§
0.92§
0.91§
0.92§
0.92§
0.92§
0.91§
0.93§
0.91§
0.91§
6 2.6
6 2.4
6 2.8
6 2.9
6 2.9
6 2.6
6 2.9
6 2.6
6 2.6
6 2.6
6 2.9
6 2.5
6 2.9
6 2.8
ICC = interclass correlation coefficient; 1RM = 1 repetition maximum.
*Predicted 1RM –Actual 1RM.
†(Predicted – Actual)/Actual 3 100.
‡p , 0.05.
§p , 0.01.
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Predicted
bench press
Mean 6 SD
Constant
error
Mean 6 SD
33.4 6 6.4‡
29.2 6 6.0‡
34.5 6 6.6‡
34.2 6 6.7‡
35.3 6 6.7
32.1 6 6.4‡
34.5 6 6.7‡
34.4 6 6.5‡
35.5 6 6.8
33.7 6 6.5‡
34.5 6 6.6‡
35.9 6 6.7
35.1 6 6.7
35.1 6 6.7
35.7 6 7.8
–2.2
–6.5
–1.1
–1.4
–0.3
–2.8
–1.1
–1.2
0.2
–2.0
–1.1
0.3
–0.6
–0.6
% Error
Mean 6 SD
6 3.6 –5.5 6 8.9
6 3.4 –17.7 6 7.4
6 3.9 –2.2 6 9.9
6 4.2 –3.1 6 10.6
6 3.5 –0.1 6 9.4
6 3.6 –7.8 6 8.7
6 4.1 –2.2 6 10.5
6 3.7 –2.5 6 9.3
6 3.5
0.5 6 9.2
6 3.6 –4.8 6 8.9
6 4.2 –2.2 6 10.4
6 3.2
1.7 6 8.7
6 4.2 –0.7 6 10.6
6 3.9 –0.7 6 10.1
ICC
0.75§
0.75§
0.74§
0.73§
0.75§
0.93§
0.73§
0.74§
0.74§
0.75§
0.91§
0.95§
0.73§
0.74§
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FIGURE 2. Comparison between the change in actual 1 repetition
maximum (1RM) bench press (DA) and the change in predicted 1RM (DP)
from the equation by Tucker (n = 103).
aspects of some of these equations may render them of limited
value in their universal application to women of various levels
of ability. The equations by Horvat et al. (18), developed on
female college athletes, used absolute weights of 55 or 70 lbs
to perform RTF in female athletes. In the current study, only
31 subjects were capable of handling 55 lbs or more for at
least 1 repetition. This would suggest that 70% of average
women cannot use the weight required for the equations by
Horvat et al. (18). The equations by Rose and Ball (32) used
untrained to moderately trained young women and absolute
weights of 35 and 45 lbs to predict 1RM. The equation by
Cosgrove and Mayhew (9) was based on the Young Men’s
Christian Association (YMCA) test (14) and used the
repetitions completed with an absolute weight of 35 lbs to
estimate 1RM. Kim et al. (22) also used the YMCA test and
had women perform their repetitions at rates of 30 and 60
repetitions per minute. There were too few subjects in the
current study using each of these weights to make
a comparison feasible. The equation by Abadie and Wentworth (2) used a load that allowed between 5 and 10
repetitions and was adequate in the pretraining sample
FIGURE 3. Comparison between the change in actual 1 repetition
maximum (1RM) bench press (DA) and the change in repetitions to
fatigue (DRTF) after training (n = 103).
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(n = 32; ICC = 0.85; t = 0.96; p . 0.05) but not in the
posttraining sample (n = 27; ICC = 0.91; t = 2.80; p , 0.05).
Although little information is available on the derivation
and statistical support for many of the prediction equations in
the literature, it may be safe to say that most were developed
by using men. This assumption obviously begs the question of
whether such equations would be accurate for use with
women. The current study indicates that when the repetitions
occurred over a wide range (i.e., 2–30), several of the
equations performed adequately in both the untrained and the
trained conditions (Table 3). Because there was a substantial
curvilinear nature to the relationship between RTF and
%1RM over a wide range of repetitions (Figure 4), it appears
that the equation by Tucker et al. (37), combining both RTF
and load, and the exponential equation by Mayhew et al. (26)
performed best. This also seems to hold true when 10 or
fewer RTF were used for prediction. That several of the
equations developed on men worked adequately on this
sample of women suggests that there is little difference
between the genders in muscular endurance capacity, despite
previous indications that women may have greater fatigue
resistance than men have (11,17,35).
A key element for success of any strength prediction
equation is whether it is able to track changes resulting from
training accurately. Mayhew et al. (27) and Sebelski et al. (34)
found no significant change in the average number of RTF
after moderate training in young men and women, but
neither study reported the degree of variation to be expected.
Abadie et al. (1) noted little change in lifting mechanics that
would influence performance after resistance training. More
recently, Duffey and Challis (11) were able to show changes
in the lifting kinematics of recreational weight trainers, as
fatigue set in during the latter stages of RTF using 75% of
1RM but made no reference to whether this would change
with training. Shimano et al. (36) found no difference
between trained and untrained men in the number of RTF
FIGURE 4. Curvilinear relationship between repetitions and percentage
of 1 repetition maximum in women (n = 103).
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Strength Prediction
performed at 60% and 80% of 1RM. However, untrained men
performed significantly more RTF at 90% of 1RM than did
trained men. The current findings on women generally
support a decrease in RTF at the upper end of the repetition
continuum (i.e., .90% 1RM), with increases in 1RM after
training, although substantial variation in the change in RTF
performed at the same %1RM was noted (95% CI, –11 to 13
repetitions). Despite minor differences when comparing DA
and DP, changes in muscle strength in women can be tracked
with acceptable accuracy by using repetition prediction
equations.
Recent research indicates that when given the opportunity
to select a weight with which to perform repetitions, many
individuals will select a lighter weight and hence perform an
excessive number of repetitions (13). Many RTF prediction
equations available in the literature have a tendency to
significantly overestimate 1RM bench press when the
repetition range is large (28). This tendency was apparent
for some of the equations in the current study, especially the
linear ones (Table 3). Previous recommendations have
suggested that a repetition range of no more than 10
produces better predictions (7,28,38). When the RTF
performed by the current participants were no more than
10, many of the equations worked adequately to predict 1RM
before or after training (Table 4).
Strength and conditioning specialists may prefer to perform
an RTF prediction rather than a 1RM assessment for women
for several reasons. An RTF assessment can be considerably
more time-efficient. After an adequate exercise-specific
warm-up, only 1 maximal set is needed when using the
RTF approach. In addition, women may not be as accustomed
to lifting heavy weights with their arms as men are, and hence,
their apprehension may prevent them from adequately
reaching a true 1RM. The current study suggests that using
RTF prediction equations can be an accurate and timeefficient way to assess maximal strength in women at various
stages along the training continuum.
Another reason often given for using a repetition equation
to predict maximal strength is safety. However, there is little
scientific literature to suggest that the 1RM technique, when
performed properly, is more dangerous than other lifting
techniques for assessing maximal strength (15,29). Indeed, it
is possible that an approach using maximal repetitions may
also have inherent dangers accompanying it. As the lifter
fatigues, the mechanics of the lift may deteriorate and place
the individual in an awkward position (11), thus offering the
potential for muscle strain or joint injury. In addition, the
fatigued condition of the lifter in the latter stages of a repetition assessment could result in an uncontrolled dropping of
the weight when she is unable to complete the last repetition.
Because of the concerns many individuals have about
strength testing, it would be wise for strength and conditioning specialists to be vigilant when having individuals
perform either a 1RM or an RTF to assess strength to ensure
lifter safety.
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Strength and conditioning specialists should also consider
the population and reason for strength testing their
participants when choosing a method to assess maximal
strength. If a precise and accurate measurement of maximal
strength is needed, for use on a strength athlete for example,
an RTF assessment may not be appropriate due to the
potential error involved with these equations. However, an
RTF assessment may be more appropriate to estimate
strength for an individual who is starting a fitness program
that includes resistance training. It may also be used
throughout the training process as a gauge of progress with
specific lifts and to allow transition between phases of
a periodization model (12).
PRACTICAL APPLICATIONS
Maximal repetition tests using a submaximal load can be used
to estimate 1RM bench press strength levels in women with
acceptable accuracy by using several existing equations. The
accuracy of these predictions appears to be enhanced if
fewer than 10 RTF are used. The use of estimated 1RM values
can allow women to track their progress more easily in
a resistance training program. The placement of prediction
charts in a training facility may encourage women to place
greater emphasis on strength development, which has been
shown to enhance bone health (20,25,33) and alter body
composition (8).
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